Signal Processing for Communication Systems
The Parseval’s theorem (a.k.a Plancherel theorem) expresses the energy of a signal in time-domain in terms of the average energy in its frequency components. Suppose if the x[n] is a discrete-time sequence of complex numbers of length N : xn={x0,x1,…,xN-1}, its N-point discrete Fourier transform (DFT)[1] : Xk={X0,X1,…,XN-1} is given by The inverse discrete Fourier … Read more
In wireless environments, transmitted signal may be subjected to multiple scatterings before arriving at the receiver. This gives rise to random fluctuations in the received signal and this phenomenon is called fading. The scattered version of the signal is designated as non line of sight (NLOS) component. If the number of NLOS components are sufficiently … Read more
Key focus: Discuss statistical measures for stochastic signals : mean, variance, skewness, kurtosis, histogram, scatterplot, cross-correlation and auto-correlation. Deterministic and stochastic signals A deterministic signal is exactly predictable for the given time span of interest. It could be expressed using analytic form (example: x(t) = sin (2 π fc t) ). Many of the signals … Read more
Key focus: Simulate bit error rate performance of Binary Phase Shift Keying (BPSK) modulation over AWGN channel using complex baseband equivalent model in Python & Matlab. Why complex baseband equivalent model The passband model and equivalent baseband model are fundamental models for simulating a communication system. In the passband model, also called as waveform simulation … Read more
The phase transition properties of the different variants of QPSK schemes and MSK, are easily investigated using constellation diagram. Let’s demonstrate how to plot the signal space constellations, for the various modulations used in the transmitter. Typically, in practical applications, the baseband modulated waveforms are passed through a pulse shaping filter for combating the phenomenon … Read more
Articles in this series Phased Array Antenna – an introduction Electronic Scanning Arrays Grating lobes in electronic scanning Array pattern multiplication (this article) Array pattern multiplication If the element pattern of an array is very broad (as in an Omni directional antenna element) the pattern of the array is mostly the Array Factor since it … Read more
The array is a periodic structure in space with elements placed at equidistant. d/λ acts as the frequency term and λ/d as the time period. The incremental phase shift between adjacent elements is (2π/λ)×d×[sin(θ)-sin(θ0)]. d is the inter-element distance in unit of λ, θ-any position during the scanning of the array and θ0 – the … Read more
Articles in this series Phased Array Antenna – an introduction Electronic Scanning Arrays (this article) Grating lobes in electronic scanning Array pattern multiplication Electronic scanning arrays This is considered to be the best feature of a phased array antenna. To be able to scan in a given space, without having to rotate the antenna is … Read more
Key focus: Phased Array Antenna, employs simpler elemental antennas to configure a complex system, has many interesting features and capabilities. Articles in this series Phased Array Antenna – an introduction (this article) Electronic Scanning Arrays Grating lobes in electronic scanning Array pattern multiplication Since the latter half of previous century, a class of antenna technology … Read more
Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability … Read more